In conventional optics, a lens can be used to refract a plane wave into a spherical wave which appears to be radiated from a point light source located at a virtual focus of the lens. Currently, the diverging effect of the lens is achieved by virtue of the refractive property of the spherical form of the lens. The inventor has found in the process of making this invention that, the lens antenna has at least the following technical problems: the lens is bulky and heavy, which is unfavorable for miniaturization; performances of the lens rely heavily on the shape thereof, and directional propagation from the antenna can be achieved only when the lens has a precise shape; and serious interferences and losses are caused to the electromagnetic waves, which reduces the electromagnetic energy. Moreover, for most lens antennae, abrupt transitions of the refractive indices follow a simple line that is perpendicular to a lens surface. Consequently, electromagnetic waves propagating through the lenses suffer from considerable refraction, diffraction and reflection, which have a serious effect on the performances of the lenses.